Question

two bodies are projected at an angle 30 and 60 to the horizontal with the same speed the ratio of times of flight is

Answer 1

Time of flight = 2 usin©/g
So use of formula

Ratio = sin30°/sin 60° = 1/root3

Answer 2

Concept:

Projectile Motion

An item or particle that is propelled toward the surface of the Earth and moves along a curved route only under the influence of gravity is said to be in projectile motion.

In a particle's vertical and horizontal projectile motion,

acceleration: A particle propelled into the air at a certain speed experiences only the acceleration brought on by gravity at this period (g). Vertically downward force is applied by this acceleration. The particle's velocity in the horizontal direction is constant because there is no acceleration in this direction.

To find:

The ratio of time of flight of the two bodies which are projected at different angles.

Given:

The angle of projection of 1st body =30°

The angle of projection of the 2nd body=60°

The initial speed of 1st body = Initial speed of 2nd body = u

Explanation:

The formula for Time of flight= 2u sin°/g

where,

g= acceleration due to gravity

u= the initial velocity of the object or body

Now, the Ratio of time of flight T' will be

T₁/T₂=2u sin30°/g÷2u sin60°/g

       =sin30°/sin60°

       =1/2÷√3/2

       =1/√3

where,

sin30°=1/2

sin60°=√3/2

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